Question

Dylan makes cupboards using wood. One of his cupboard designs is made from:

3 small panels 550 mm by 550 mm
4 large panels 2150 mm by 550 mm.
The boards used to cut the panels are 2500 mm by 2000 mm. There must be no joins in the panels. Dylan has an order for 6 of these cupboards. He buys 9 boards to cut the panels. Has Dylan bought enough wooden boards? Show why you think this. You may use diagrams.
a) Yes, Dylan has enough boards
b) No, Dylan needs more boards
c) It depends on the cutting efficiency
d) Insufficient information to determine

Answer 1

To determine if Dylan has enough wooden boards, we calculate the total area required for the panels and compare it to the total area of the boards he bought. The answer is yes, Dylan has enough boards.

Step-by-step explanation:

To determine if Dylan has bought enough wooden boards, we need to calculate the total area required for the panels in all 6 cupboards and compare it to the total area of the boards he bought.

First, let's calculate the area of the small panels: 550 mm * 550 mm * 3 = 907,500 mm². Similarly, the area of the large panels is 2150 mm * 550 mm * 4 = 5,610,000 mm².

Adding the areas of all the panels gives a total area of 6,517,500 mm². To convert this to square meters, we divide by 1,000,000: 6,517,500 mm² / 1,000,000 = 6.5175 m².

Each board has an area of 2500 mm * 2000 mm = 5,000,000 mm², which is equivalent to 5 m². Dylan bought 9 boards, so the total area of the boards is 5 m² * 9 = 45 m².

Since the total area of the panels is 6.5175 m² and Dylan bought 45 m² of boards, it is clear that Dylan has enough wooden boards. Therefore, the answer is a) Yes, Dylan has enough boards.